Analyses for ‘Don’t Stress, It’s Under Control: Neural Correlates of Stressor Controllability in Humans’
Laura E. Meine & Jana Meier
18.02.2021
1 Script Overview
Built with R 3.6.2
This script runs analyses on data from the SPECTRE study. Specifically, it investigates different read-outs as a function of whether participants experienced controllable or uncontrollable stress (or no stress). Measurements under investigation comprised participant ratings (stressor aversiveness, perceived control, stress, helplessness), reaction times, correct responses, and heart rates. In addition, MR parameter estimates from a GLM analysis of related imaging data were investigated and linked to the ratings.
Here we use the following abbreviations: controllable stress = con; uncontrollable stress = noc, baseline = bas.
Linear mixed-effects models were constructed based on the tutorial referenced in Singmann & Kellen, 2019: https://cran.r-project.org/web/packages/afex/vignettes/afex_mixed_example.html
2 Sample Descriptives
N = 45 participants aged 19-30 took part in this study (46.67 % female, age: M = 25, SD = 3.05).
3 Manipulation Checks
3.1 Version Counterbalancing
##
## 1 2 3 4 5 6
## 8 8 8 8 6 73.2 Yoking of Stress Durations
##
## Paired t-test
##
## data: stressDur$total_con_stress_dur and stressDur$total_noc_stress_dur
## t = 6.3263, df = 44, p-value = 1.117e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1.178446 2.280295
## sample estimates:
## mean of the differences
## 1.72937##
## Cohen's d
##
## d estimate: 1.004407 (large)
## 95 percent confidence interval:
## lower upper
## 0.559817 1.448996## [1] 1.833766There was a significant difference in overall stress duration between conditions, yoking did not work out properly. Participants were on average exposed to LESS stress in the uncontrollable condition but reported experiencing no difference or even MORE stress in this condition when asked afterwards. Therefore, effects showing greater performance decrements associated with uncontrollable stress cannot be attributed to more stress. Nevertheless, this remains a limitation and the CON-UNCON stress duration difference is therefore included as a covariate in subsequent analyses.
3.3 Stressor Aversiveness
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## aversiveness ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2512.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8204 -0.4590 -0.0135 0.5387 3.1386
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 2.123e+02 14.56928
## condition1 9.658e-03 0.09827 0.24
## run.z 4.903e+01 7.00240 0.45 0.97
## stress_dur_diff.z 3.962e+00 1.99037 -0.99 -0.36 -0.56
## condition1:run.z 1.192e-01 0.34524 0.42 0.98 1.00 -0.54
## Residual 3.107e+01 5.57371
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 64.2346 2.1160 33.6567 30.356 < 2e-16 ***
## condition1 -0.4302 0.2958 257.4147 -1.455 0.14702
## run.z -3.6294 1.0812 44.4496 -3.357 0.00162 **
## condition1:run.z -0.2053 0.3002 204.2381 -0.684 0.49488
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 0.011
## run.z 0.415 0.047
## cndtn1:rn.z 0.069 0.008 0.164
## convergence code: 1
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z +
## re1.stress_dur_diff.z + re1.condition1_by_run.z || id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2523
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9451 -0.4570 -0.0275 0.5309 3.1533
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 210.14 14.496
## id.1 re1.condition1 0.00 0.000
## id.2 re1.run.z 49.07 7.005
## id.3 re1.stress_dur_diff.z 0.00 0.000
## id.4 re1.condition1_by_run.z 0.00 0.000
## Residual 31.25 5.590
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 63.8372 2.1816 43.8455 29.261 < 2e-16 ***
## condition1 -0.4354 0.2963 264.1050 -1.470 0.14286
## run.z -3.7103 1.0871 44.1177 -3.413 0.00139 **
## condition1:run.z -0.2151 0.2967 264.1050 -0.725 0.46901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 0.000
## run.z 0.001 0.000
## cndtn1:rn.z 0.000 0.000 0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 14.4963
## id.1 re1.condition1 0.0000
## id.2 re1.run.z 7.0047
## id.3 re1.stress_dur_diff.z 0.0000
## id.4 re1.condition1_by_run.z 0.0000
## Residual 5.5899## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + re1.condition1 + re1.run.z +
## re1.stress_dur_diff.z || id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2523
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9451 -0.4570 -0.0275 0.5309 3.1533
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 2.101e+02 1.450e+01
## id.1 re1.condition1 0.000e+00 0.000e+00
## id.2 re1.run.z 4.907e+01 7.005e+00
## id.3 re1.stress_dur_diff.z 3.523e-13 5.936e-07
## Residual 3.125e+01 5.590e+00
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 63.8372 2.1816 43.8455 29.261 < 2e-16 ***
## condition1 -0.4354 0.2963 264.1050 -1.470 0.14286
## run.z -3.7103 1.0871 44.1177 -3.413 0.00139 **
## condition1:run.z -0.2151 0.2967 264.1050 -0.725 0.46901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 0.000
## run.z 0.001 0.000
## cndtn1:rn.z 0.000 0.000 0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 1.4496e+01
## id.1 re1.condition1 0.0000e+00
## id.2 re1.run.z 7.0047e+00
## id.3 re1.stress_dur_diff.z 5.9355e-07
## Residual 5.5899e+00## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + run.z + stress_dur_diff.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2523
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9451 -0.4570 -0.0275 0.5309 3.1533
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 2.101e+02 1.450e+01
## id.1 run.z 4.907e+01 7.005e+00
## id.2 stress_dur_diff.z 7.766e-15 8.813e-08
## Residual 3.125e+01 5.590e+00
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 63.8372 2.1816 43.8455 29.261 < 2e-16 ***
## condition1 -0.4354 0.2963 264.1050 -1.470 0.14286
## run.z -3.7103 1.0871 44.1177 -3.413 0.00139 **
## condition1:run.z -0.2151 0.2967 264.1050 -0.725 0.46901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 0.000
## run.z 0.001 0.000
## cndtn1:rn.z 0.000 0.000 0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: aversiveness ~ condition * run.z + (1 + run.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2515.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9268 -0.4541 -0.0162 0.5456 3.1957
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 211.18 14.532
## run.z 49.01 7.001 0.42
## Residual 31.24 5.590
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 63.8377 2.1869 43.8362 29.191 < 2e-16 ***
## condition1 -0.4354 0.2962 264.1496 -1.470 0.14284
## run.z -3.7096 1.0865 44.1244 -3.414 0.00138 **
## condition1:run.z -0.2151 0.2967 264.1496 -0.725 0.46899
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 0.000
## run.z 0.398 0.000
## cndtn1:rn.z 0.000 0.000 0.000
## $id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Data: data
## Models:
## avers.m4c: aversiveness ~ condition * run.z + (1 + run.z | id)
## avers.maxc: aversiveness ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |
## avers.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## avers.m4c 8 2535.5 2566.5 -1259.8 2519.5
## avers.maxc 20 2556.3 2633.8 -1258.2 2516.3 3.1834 12 0.9941| Fixed Effects - Stressor Aversiveness | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 63.84 | 59.55 – 68.12 | <0.001 |
| Condition | -0.44 | -1.02 – 0.15 | 0.143 |
| Run | -3.71 | -5.84 – -1.58 | 0.001 |
| Condition x Run | -0.22 | -0.80 – 0.37 | 0.469 |
| Random Effects | |||
| σ2 | 31.24 | ||
| τ00 id | 211.18 | ||
| τ11 id.run.z | 49.01 | ||
| ρ01 id | 0.42 | ||
| ICC | 0.89 | ||
| N id | 45 | ||
| Marginal R2 / Conditional R2 | 0.046 / 0.898 | ||
Participants rated the stressor as very aversive in both controllable and uncontrollable trials (global M = 63.75). In both conditions, aversiveness ratings decreased slightly over runs.
3.4 Perceived Control
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3030.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2040 -0.4675 0.0540 0.4761 3.0614
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 6.161 2.482
## condition1 95.580 9.776 -0.50
## run.z 35.038 5.919 -0.22 -0.03
## stress_dur_diff.z 187.870 13.707 -0.79 -0.09 0.05
## condition1:run.z 14.140 3.760 -0.29 0.59 -0.29 -0.06
## Residual 163.912 12.803
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.6964 1.3223 71.6054 35.315 < 2e-16 ***
## condition1 16.4062 1.6051 44.1879 10.221 3.23e-13 ***
## run.z 0.8908 1.1165 40.3465 0.798 0.4297
## condition1:run.z 1.7884 0.8843 44.3610 2.023 0.0492 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 -0.123
## run.z -0.044 -0.021
## cndtn1:rn.z -0.051 0.342 -0.147
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3039
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3188 -0.4210 0.0349 0.5060 3.0524
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 0.2108 0.4592
## id.1 conditioncon 89.4320 9.4568
## conditionnoc 126.5411 11.2490 -0.79
## id.2 run.z 22.8396 4.7791
## id.3 stress_dur_diff.z 190.2152 13.7919
## id.4 conditioncon:run.z 13.1683 3.6288
## conditionnoc:run.z 39.9533 6.3209 -0.07
## Residual 164.6075 12.8299
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.6816 1.3809 14.6523 33.806 2.58e-15 ***
## condition1 16.4389 1.6108 44.2287 10.206 3.34e-13 ***
## run.z 0.8883 1.1207 40.4252 0.793 0.4326
## condition1:run.z 1.7870 0.8845 44.4677 2.020 0.0494 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 -0.093
## run.z 0.008 0.000
## cndtn1:rn.z -0.001 0.003 -0.151
## convergence code: 0
## Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?## Groups Name Std.Dev. Corr
## id (Intercept) 0.45917
## id.1 conditioncon 9.45685
## conditionnoc 11.24905 -0.786
## id.2 run.z 4.77908
## id.3 stress_dur_diff.z 13.79185
## id.4 conditioncon:run.z 3.62882
## conditionnoc:run.z 6.32086 -0.069
## Residual 12.82995## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## control ~ condition * run.z + (1 + condition + run.z + stress_dur_diff.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3045.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2505 -0.4610 0.0405 0.4961 3.6482
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 1.283e-09 3.582e-05
## id.1 conditioncon 8.433e+01 9.183e+00
## conditionnoc 1.216e+02 1.103e+01 -0.83
## id.2 run.z 3.223e+01 5.678e+00
## id.3 stress_dur_diff.z 1.904e+02 1.380e+01
## Residual 1.868e+02 1.367e+01
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.6663 1.3827 14.5964 33.750 2.91e-15 ***
## condition1 16.4454 1.6122 44.2038 10.200 3.42e-13 ***
## run.z 0.8747 1.1179 40.3191 0.782 0.4385
## condition1:run.z 1.7959 0.7272 218.9354 2.470 0.0143 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 -0.093
## run.z 0.008 0.000
## cndtn1:rn.z 0.000 0.002 0.000
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev. Corr
## id (Intercept) 3.5817e-05
## id.1 conditioncon 9.1833e+00
## conditionnoc 1.1028e+01 -0.825
## id.2 run.z 5.6775e+00
## id.3 stress_dur_diff.z 1.3797e+01
## Residual 1.3668e+01## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: control ~ condition * run.z + (1 + condition + run.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3051.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3566 -0.4820 0.0051 0.4759 3.5258
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 128.08 11.317
## condition1 93.24 9.656 -0.06
## run.z 31.99 5.656 0.27 -0.04
## Residual 187.17 13.681
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 48.2104 1.8378 44.2242 26.233 < 2e-16 ***
## condition1 16.4441 1.6122 44.2044 10.200 3.43e-13 ***
## run.z 0.8685 1.1173 39.6417 0.777 0.4416
## condition1:run.z 1.7941 0.7279 217.7533 2.465 0.0145 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 run.z
## condition1 -0.050
## run.z 0.190 -0.024
## cndtn1:rn.z 0.000 0.002 0.000
## $id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Data: data
## Models:
## ctrl.m3c: control ~ condition * run.z + (1 + condition + run.z | id)
## ctrl.maxc: control ~ condition * run.z + (1 + condition * run.z + stress_dur_diff.z |
## ctrl.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## ctrl.m3c 11 3082.6 3125.2 -1530.3 3060.6
## ctrl.maxc 20 3079.4 3156.9 -1519.7 3039.4 21.253 9 0.01157 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| Fixed Effects - Perceived Control | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 48.21 | 44.61 – 51.81 | <0.001 |
| Condition | 16.44 | 13.28 – 19.60 | <0.001 |
| Run | 0.87 | -1.32 – 3.06 | 0.442 |
| Condition x Run | 1.79 | 0.37 – 3.22 | 0.014 |
| Random Effects | |||
| σ2 | 187.17 | ||
| τ00 id | 128.08 | ||
| τ11 id.condition1 | 93.24 | ||
| τ11 id.run.z | 31.99 | ||
| ρ01 | -0.06 | ||
| 0.27 | |||
| ICC | 0.57 | ||
| N id | 45 | ||
| Marginal R2 / Conditional R2 | 0.385 / 0.738 | ||
Participants reported higher perceived control under controllable trials compared to uncontrollable trials. Ratings increased over runs for controllable stress, but decreased for uncontrollable stress.
4 Ratings
4.1 Stress
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 4260.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9213 -0.4045 -0.0382 0.3733 4.3181
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 255.815 15.994
## condition1 179.777 13.408 -0.26
## condition2 65.848 8.115 0.22 -0.78
## run.z 24.979 4.998 0.15 0.13 0.01
## stress_dur_diff.z 33.751 5.810 0.54 -0.72 0.26 -0.42
## condition1:run.z 7.812 2.795 -0.51 0.05 -0.11 -0.92 0.10
## condition2:run.z 2.466 1.570 0.20 -0.02 0.58 0.55 -0.48
## Residual 81.139 9.008
##
##
##
##
##
##
##
## -0.52
##
## Number of obs: 534, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 39.904 2.206 36.262 18.093 < 2e-16 ***
## condition1 -17.610 2.005 41.349 -8.783 5.33e-11 ***
## condition2 7.414 1.294 44.055 5.729 8.39e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 -0.196
## condition2 0.185 -0.766
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## stress ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +
## re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 4323.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4502 -0.3849 -0.0329 0.3338 4.0466
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 266.691 16.331
## id.1 re1.condition1 162.838 12.761
## id.2 re1.condition2 58.278 7.634
## id.3 re1.run.z 24.409 4.941
## id.4 re1.stress_dur_diff.z 0.000 0.000
## id.5 re1.condition1_by_run.z 5.207 2.282
## id.6 re1.condition2_by_run.z 0.000 0.000
## Residual 85.267 9.234
## Number of obs: 534, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 36.930 2.468 44.014 14.967 < 2e-16 ***
## condition1 -18.246 1.985 43.951 -9.193 8.48e-12 ***
## condition2 7.110 1.271 44.057 5.595 1.32e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.000
## condition2 0.000 -0.063
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 16.3307
## id.1 re1.condition1 12.7608
## id.2 re1.condition2 7.6340
## id.3 re1.run.z 4.9406
## id.4 re1.stress_dur_diff.z 0.0000
## id.5 re1.condition1_by_run.z 2.2820
## id.6 re1.condition2_by_run.z 0.0000
## Residual 9.2340## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition + run.z + stress_dur_diff.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 4292.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5256 -0.3841 -0.0554 0.3751 4.1937
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 193.85 13.923
## id.1 conditionbas 146.03 12.084
## conditioncon 189.47 13.765 -0.24
## conditionnoc 200.17 14.148 -0.28 0.75
## id.2 run.z 23.96 4.895
## id.3 stress_dur_diff.z 0.00 0.000
## Residual 89.42 9.456
## Number of obs: 534, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 36.931 2.468 44.014 14.962 < 2e-16 ***
## condition1 -18.223 2.079 44.003 -8.766 3.30e-11 ***
## condition2 7.121 1.330 44.098 5.352 2.97e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 -0.229
## condition2 0.177 -0.744
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev. Corr
## id (Intercept) 13.923
## id.1 conditionbas 12.084
## conditioncon 13.765 -0.236
## conditionnoc 14.148 -0.280 0.750
## id.2 run.z 4.895
## id.3 stress_dur_diff.z 0.000
## Residual 9.456## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition + (1 + condition + run.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 4290.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5270 -0.3883 -0.0462 0.3709 4.1945
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 267.24 16.347
## condition1 180.09 13.420 -0.24
## condition2 64.51 8.032 0.20 -0.79
## run.z 23.98 4.897 0.14 0.15 -0.01
## Residual 89.41 9.456
## Number of obs: 534, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 37.888 2.453 43.999 15.443 < 2e-16 ***
## condition1 -17.387 2.067 44.034 -8.412 1.04e-10 ***
## condition2 7.098 1.330 44.102 5.336 3.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 -0.244
## condition2 0.178 -0.748
## $id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Data: data
## Models:
## stress.m3c: stress ~ condition + (1 + condition + run.z | id)
## stress.maxc: stress ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## stress.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## stress.m3c 14 4327.4 4387.3 -2149.7 4299.4
## stress.maxc 32 4332.5 4469.5 -2134.2 4268.5 30.873 18 0.02977 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## condition emmean SE df lower.CL upper.CL
## bas 20.5 2.86 44 14.7 26.3
## con 45.0 3.06 44 38.8 51.2
## noc 48.2 3.11 44 41.9 54.4
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## bas - con -24.48 3.26 44 -7.515 <.0001
## bas - noc -27.68 3.33 44 -8.300 <.0001
## con - noc -3.19 1.81 44 -1.765 0.0845
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: holm method for 3 tests| Fixed Effects - Stress | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 37.89 | 33.08 – 42.70 | <0.001 |
| Condition-CON | -17.39 | -21.44 – -13.34 | <0.001 |
| Condition-UNCON | 7.10 | 4.49 – 9.70 | <0.001 |
| Random Effects | |||
| σ2 | 89.41 | ||
| τ00 id | 267.24 | ||
| τ11 id.condition1 | 180.09 | ||
| τ11 id.condition2 | 64.51 | ||
| τ11 id.run.z | 23.98 | ||
| ρ01 | -0.24 | ||
| 0.20 | |||
| 0.14 | |||
| ICC | 0.81 | ||
| N id | 45 | ||
| Marginal R2 / Conditional R2 | 0.249 / 0.855 | ||
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## stress ~ condition * aversiveness.z + (1 + condition * aversiveness.z +
## run.z | id) + (1 | run)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2869.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9148 -0.3764 -0.0081 0.3585 3.8930
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 292.120 17.092
## condition1 13.650 3.695 -0.12
## aversiveness.z 46.175 6.795 -0.31 -0.64
## run.z 20.166 4.491 -0.18 0.31 0.44
## condition1:aversiveness.z 8.834 2.972 0.48 0.70 -0.95 -0.28
## run (Intercept) 0.000 0.000
## Residual 101.356 10.068
## Number of obs: 356, groups: id, 45; run, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.7521 2.6390 41.1145 17.716 < 2e-16 ***
## condition1 -2.3315 0.7898 42.4631 -2.952 0.00513 **
## aversiveness.z 4.9076 1.5789 23.0594 3.108 0.00494 **
## condition1:aversiveness.z 1.0953 0.7849 36.2080 1.395 0.17138
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 avrsv.
## condition1 -0.112
## aversvnss.z -0.179 -0.255
## cndtn1:vrs. 0.222 0.335 -0.467
## convergence code: 0
## boundary (singular) fit: see ?isSingularParticipants reported higher stress levels in both stress conditions compared to baseline. There was no difference in stress ratings between controllable and uncontrollable stress trials.
4.2 Helplessness
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## helplessness ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3098.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.94407 -0.42820 -0.03208 0.38843 2.75336
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 240.026 15.493
## condition1 138.447 11.766 -0.09
## run.z 36.607 6.050 -0.03 -0.13
## stress_dur_diff.z 88.438 9.404 0.13 0.51 -0.22
## condition1:run.z 8.119 2.849 -0.22 0.46 0.03 0.46
## Residual 172.909 13.149
## Number of obs: 356, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 45.781 2.556 32.288 17.909 < 2e-16 ***
## condition1 -10.502 1.800 40.648 -5.833 7.68e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## condition1 -0.101
## $id
| Fixed Effects - Helplessness | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 45.78 | 40.77 – 50.79 | <0.001 |
| Condition | -10.50 | -14.03 – -6.97 | <0.001 |
| Random Effects | |||
| σ2 | 172.91 | ||
| τ00 id | 240.03 | ||
| τ11 id.condition1 | 138.45 | ||
| τ11 id.run.z | 36.61 | ||
| τ11 id.stress_dur_diff.z | 88.44 | ||
| τ11 id.condition1:run.z | 8.12 | ||
| ρ01 | -0.09 | ||
| -0.03 | |||
| 0.13 | |||
| -0.22 | |||
| ICC | 0.69 | ||
| N id | 45 | ||
| Marginal R2 / Conditional R2 | 0.167 / 0.739 | ||
Participants reported feeling less helpless in controllable trials compared to uncontrollable trials.
5 Reaction Times (RT)
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + condition * run.z + stress_dur_diff.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 58659.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1193 -0.6576 -0.0151 0.6336 3.3257
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 989.67 31.459
## condition1 309.79 17.601 -0.46
## condition2 71.98 8.484 0.44 -0.99
## run.z 71.19 8.437 0.45 0.16 -0.24
## stress_dur_diff.z 1509.89 38.857 0.06 0.36 -0.32 -0.16
## condition1:run.z 131.62 11.473 0.08 -0.23 0.23 -0.33 0.72
## condition2:run.z 50.44 7.102 -0.08 -0.02 -0.07 0.65 -0.69
## Residual 10574.83 102.834
##
##
##
##
##
##
##
## -0.46
##
## Number of obs: 4830, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 768.500 5.759 36.296 133.449 < 2e-16 ***
## condition1 17.527 3.532 41.791 4.962 1.22e-05 ***
## condition2 -26.592 2.389 68.600 -11.129 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 -0.302
## condition2 0.205 -0.724
## convergence code: 1
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +
## re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 58685.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0492 -0.6560 -0.0204 0.6269 3.3666
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1072.77 32.753
## id.1 re1.condition1 120.43 10.974
## id.2 re1.condition2 0.00 0.000
## id.3 re1.run.z 84.43 9.188
## id.4 re1.stress_dur_diff.z 1317.37 36.296
## id.5 re1.condition1_by_run.z 103.03 10.151
## id.6 re1.condition2_by_run.z 17.63 4.199
## Residual 10632.30 103.113
## Number of obs: 4830, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 768.446 6.369 39.072 120.654 < 2e-16 ***
## condition1 18.784 3.029 77.844 6.202 2.5e-08 ***
## condition2 -27.105 2.078 4675.124 -13.043 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.073
## condition2 -0.055 -0.511
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +
## re1.stress_dur_diff.z || id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 58691.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0612 -0.6505 -0.0200 0.6333 3.2452
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.072e+03 3.275e+01
## id.1 re1.condition1 1.195e+02 1.093e+01
## id.2 re1.condition2 1.209e-11 3.478e-06
## id.3 re1.run.z 8.913e+01 9.441e+00
## id.4 re1.stress_dur_diff.z 1.313e+03 3.624e+01
## Residual 1.070e+04 1.035e+02
## Number of obs: 4830, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 768.417 6.367 39.075 120.686 < 2e-16 ***
## condition1 18.732 3.028 78.092 6.186 2.64e-08 ***
## condition2 -27.090 2.084 4708.688 -13.002 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.073
## condition2 -0.055 -0.512
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 3.2747e+01
## id.1 re1.condition1 1.0931e+01
## id.2 re1.condition2 3.4776e-06
## id.3 re1.run.z 9.4409e+00
## id.4 re1.stress_dur_diff.z 3.6237e+01
## Residual 1.0346e+02## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: rt ~ condition + (1 + run.z + stress_dur_diff.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 58695.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.05636 -0.65107 -0.01586 0.64175 3.15451
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 1038.02 32.218
## run.z 84.66 9.201 0.37
## stress_dur_diff.z 1502.20 38.758 -0.02 -0.36
## Residual 10767.54 103.767
## Number of obs: 4830, groups: id, 45
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 769.377 6.172 38.024 124.653 < 2e-16 ***
## condition1 18.648 2.552 4745.939 7.306 3.21e-13 ***
## condition2 -27.038 2.089 4742.534 -12.943 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.089
## condition2 -0.055 -0.609
## $id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Data: data
## Models:
## rt.m3c: rt ~ condition + (1 + run.z + stress_dur_diff.z | id)
## rt.maxc: rt ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## rt.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## rt.m3c 10 58727 58792 -29354 58707
## rt.maxc 32 58736 58944 -29336 58672 34.809 22 0.04056 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## condition emmean SE df asymp.LCL asymp.UCL
## bas 788 6.89 Inf 775 802
## con 742 6.41 Inf 730 755
## noc 778 6.41 Inf 765 790
##
## Degrees-of-freedom method: asymptotic
## Confidence level used: 0.95## contrast estimate SE df z.ratio p.value
## bas - con 45.7 4.17 Inf 10.962 <.0001
## bas - noc 10.3 4.18 Inf 2.456 0.0140
## con - noc -35.4 3.31 Inf -10.688 <.0001
##
## Degrees-of-freedom method: asymptotic
## P value adjustment: holm method for 3 tests| Fixed Effects - Reaction Times | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 769.38 | 757.28 – 781.47 | <0.001 |
| Condition-CON | 18.65 | 13.65 – 23.65 | <0.001 |
| Condition-UNCON | -27.04 | -31.13 – -22.94 | <0.001 |
| Random Effects | |||
| σ2 | 10767.54 | ||
| τ00 id | 1038.02 | ||
| τ11 id.run.z | 84.66 | ||
| τ11 id.stress_dur_diff.z | 1502.20 | ||
| ρ01 | 0.37 | ||
| -0.02 | |||
| ICC | 0.09 | ||
| N id | 45 | ||
| Marginal R2 / Conditional R2 | 0.031 / 0.116 | ||
Reaction times were shorter under stress compared to baseline. Further, participants responded faster in the controllable condition compared to the uncontrollable condition.
6 Correct Responses
## Fitting 2 (g)lmer() models:
## [..]## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## AIC BIC logLik deviance df.resid
## 3639.8 3842.4 -1788.9 3577.8 5068
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.0043 0.2166 0.3055 0.3808 0.9227
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 0.13826 0.3718
## condition1 0.06058 0.2461 -0.28
## condition2 0.06208 0.2492 -0.42 -0.75
## run.z 0.10555 0.3249 0.62 -0.91 0.43
## stress_dur_diff.z 0.43368 0.6585 -0.58 0.94 -0.49 -0.97
## condition1:run.z 0.06074 0.2464 -0.07 0.90 -0.79 -0.81 0.74
## condition2:run.z 0.09416 0.3069 0.06 -0.85 0.76 0.63 -0.79 -0.60
## Number of obs: 5099, groups: id, 44
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.9245 0.1617 11.902 <2e-16 ***
## condition1 -0.2031 0.1259 -1.614 0.1066
## condition2 0.2300 0.1219 1.887 0.0591 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 -0.045
## condition2 -0.316 -0.528
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting 2 (g)lmer() models:
## [..]## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ condition + (1 + re1.condition1 + re1.condition2 +
## re1.run.z + re1.stress_dur_diff.z + re1.condition1_by_run.z +
## re1.condition2_by_run.z || id)
## Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## AIC BIC logLik deviance df.resid
## 3632.1 3697.5 -1806.1 3612.1 5089
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.2326 0.2325 0.3034 0.3907 0.9230
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1712604 0.41384
## id.1 re1.condition1 0.0003078 0.01754
## id.2 re1.condition2 0.0000000 0.00000
## id.3 re1.run.z 0.0584192 0.24170
## id.4 re1.stress_dur_diff.z 0.3524759 0.59370
## id.5 re1.condition1_by_run.z 0.0157318 0.12543
## id.6 re1.condition2_by_run.z 0.0493952 0.22225
## Number of obs: 5099, groups: id, 44
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.08868 0.10831 19.285 < 2e-16 ***
## condition1 -0.32451 0.06750 -4.807 1.53e-06 ***
## condition2 0.30690 0.06335 4.844 1.27e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.057
## condition2 -0.007 -0.574
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 0.413836
## id.1 re1.condition1 0.017545
## id.2 re1.condition2 0.000000
## id.3 re1.run.z 0.241701
## id.4 re1.stress_dur_diff.z 0.593697
## id.5 re1.condition1_by_run.z 0.125427
## id.6 re1.condition2_by_run.z 0.222250## Fitting 2 (g)lmer() models:
## [..]## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ condition + (1 + condition + run.z + stress_dur_diff.z ||
## id)
## Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## AIC BIC logLik deviance df.resid
## 3636.3 3714.7 -1806.1 3612.3 5087
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.7146 0.2333 0.3053 0.3847 0.9688
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 1.683e-13 4.102e-07
## id.1 conditionbas 1.181e-01 3.437e-01
## conditioncon 4.848e-02 2.202e-01 1.00
## conditionnoc 2.516e-01 5.016e-01 1.00 1.00
## id.2 run.z 5.914e-02 2.432e-01
## id.3 stress_dur_diff.z 4.324e-01 6.576e-01
## Number of obs: 5099, groups: id, 44
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.04907 0.10341 19.815 < 2e-16 ***
## condition1 -0.31784 0.06989 -4.548 5.42e-06 ***
## condition2 0.27516 0.06694 4.110 3.95e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.072
## condition2 -0.203 -0.521
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev. Corr
## id (Intercept) 4.1019e-07
## id.1 conditionbas 3.4368e-01
## conditioncon 2.2018e-01 1.000
## conditionnoc 5.0159e-01 1.000 1.000
## id.2 run.z 2.4320e-01
## id.3 stress_dur_diff.z 6.5756e-01## Fitting 2 (g)lmer() models:
## [..]## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ condition + (1 + condition + stress_dur_diff.z || id)
## Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## AIC BIC logLik deviance df.resid
## 3642.1 3714.0 -1810.1 3620.1 5088
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.6926 0.2298 0.3099 0.3859 0.8294
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 8.694e-14 2.949e-07
## id.1 conditionbas 1.129e-01 3.360e-01
## conditioncon 4.718e-02 2.172e-01 1.00
## conditionnoc 2.465e-01 4.965e-01 1.00 1.00
## id.2 stress_dur_diff.z 4.384e-01 6.621e-01
## Number of obs: 5099, groups: id, 44
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.02673 0.10241 19.789 < 2e-16 ***
## condition1 -0.31598 0.06982 -4.525 6.03e-06 ***
## condition2 0.27365 0.06680 4.096 4.20e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.069
## condition2 -0.201 -0.519
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting 2 (g)lmer() models:
## [..]## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ condition + (1 + stress_dur_diff.z || id)
## Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## AIC BIC logLik deviance df.resid
## 3634.5 3667.1 -1812.2 3624.5 5094
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.3455 0.2389 0.3074 0.3936 0.8272
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.1672 0.4089
## id.1 stress_dur_diff.z 0.3577 0.5981
## Number of obs: 5099, groups: id, 44
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.05032 0.10725 19.117 < 2e-16 ***
## condition1 -0.30968 0.06692 -4.628 3.69e-06 ***
## condition2 0.30177 0.06209 4.860 1.17e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.067
## condition2 -0.007 -0.582
## $id
## Fitting 2 (g)lmer() models:
## [..]## Fitting 2 (g)lmer() models:
## [..]## Data: data
## Models:
## corr.m4c: correct ~ condition + (1 + stress_dur_diff.z || id)
## corr.maxc: correct ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## corr.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## corr.m4c 5 3634.5 3667.1 -1812.2 3624.5
## corr.maxc 31 3639.8 3842.4 -1788.9 3577.8 46.687 26 0.007636 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## condition emmean SE df asymp.LCL asymp.UCL
## bas 1.74 0.130 Inf 1.49 2.00
## con 2.35 0.124 Inf 2.11 2.59
## noc 2.06 0.119 Inf 1.83 2.29
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95## contrast estimate SE df z.ratio p.value
## bas - con -0.611 0.115 Inf -5.329 <.0001
## bas - noc -0.318 0.110 Inf -2.887 0.0073
## con - noc 0.294 0.101 Inf 2.905 0.0073
##
## Results are given on the log odds ratio (not the response) scale.
## P value adjustment: holm method for 3 tests| Fixed Effects - Correct Responses | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 2.05 | 1.84 – 2.26 | <0.001 |
| Condition-CON | -0.31 | -0.44 – -0.18 | <0.001 |
| Condition-UNCON | 0.30 | 0.18 – 0.42 | <0.001 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 id | 0.17 | ||
| τ00 id.1 | 0.36 | ||
| ICC | 0.05 | ||
| N id | 44 | ||
| Marginal R2 / Conditional R2 | 0.015 / 0.062 | ||
Performance was significantly better (higher rate of correct responses) under stress compared to baseline. Further, participants responded correctly more often in the controllable condition compared to the uncontrollable condition.
7 Heart Rate (HR)
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2469.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8383 -0.4901 -0.0126 0.4777 6.6188
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 128.5617 11.3385
## condition1 0.1935 0.4399 -0.11
## condition2 0.1867 0.4321 0.41 -0.95
## run.z 8.3145 2.8835 -0.47 0.93 -1.00
## stress_dur_diff.z 12.1787 3.4898 0.80 0.11 0.14 -0.22
## condition1:run.z 0.1235 0.3514 0.83 -0.60 0.81 -0.86 0.67
## condition2:run.z 0.4259 0.6526 -0.58 0.87 -0.98 0.99 -0.33
## Residual 5.9810 2.4456
##
##
##
##
##
##
##
## -0.91
##
## Number of obs: 462, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 60.2838 1.4482 33.2819 41.627 <2e-16 ***
## condition1 -0.2322 0.1636 269.1272 -1.420 0.157
## condition2 0.2107 0.1620 360.2372 1.301 0.194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.127
## condition2 -0.008 -0.504
## convergence code: 1
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.condition1 + re1.condition2 + re1.run.z +
## re1.stress_dur_diff.z + re1.condition1_by_run.z + re1.condition2_by_run.z ||
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2496.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5023 -0.4937 -0.0187 0.4300 6.5337
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 1.058e+02 1.029e+01
## id.1 re1.condition1 0.000e+00 0.000e+00
## id.2 re1.condition2 0.000e+00 0.000e+00
## id.3 re1.run.z 8.187e+00 2.861e+00
## id.4 re1.stress_dur_diff.z 1.372e+01 3.704e+00
## id.5 re1.condition1_by_run.z 0.000e+00 0.000e+00
## id.6 re1.condition2_by_run.z 1.269e-14 1.126e-07
## Residual 6.353e+00 2.520e+00
## Number of obs: 462, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 64.4401 1.6708 40.7322 38.569 < 2e-16 ***
## condition1 -0.5347 0.1658 375.8336 -3.224 0.00137 **
## condition2 0.5405 0.1658 375.8336 3.259 0.00122 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.000
## condition2 0.000 -0.500
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev.
## id (Intercept) 1.0288e+01
## id.1 re1.condition1 0.0000e+00
## id.2 re1.condition2 0.0000e+00
## id.3 re1.run.z 2.8612e+00
## id.4 re1.stress_dur_diff.z 3.7036e+00
## id.5 re1.condition1_by_run.z 0.0000e+00
## id.6 re1.condition2_by_run.z 1.1263e-07
## Residual 2.5205e+00## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bpm ~ condition + (1 + re1.run.z + re1.stress_dur_diff.z || id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2496.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5023 -0.4937 -0.0187 0.4300 6.5337
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 105.846 10.288
## id.1 re1.run.z 8.187 2.861
## id.2 re1.stress_dur_diff.z 13.717 3.704
## Residual 6.353 2.520
## Number of obs: 462, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 64.4401 1.6708 40.7322 38.569 < 2e-16 ***
## condition1 -0.5347 0.1658 375.8336 -3.224 0.00137 **
## condition2 0.5405 0.1658 375.8336 3.259 0.00122 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1
## condition1 0.000
## condition2 0.000 -0.500
## $id
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Data: data
## Models:
## hr.m2c: bpm ~ condition + (1 + re1.run.z + re1.stress_dur_diff.z || id)
## hr.maxc: bpm ~ condition + (1 + condition * run.z + stress_dur_diff.z |
## hr.maxc: id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## hr.m2c 7 2509.2 2538.2 -1247.6 2495.2
## hr.maxc 32 2531.9 2664.2 -1233.9 2467.9 27.344 25 0.3389## condition emmean SE df lower.CL upper.CL
## bas 63.9 1.73 41.1 60.4 67.4
## con 65.0 1.73 41.1 61.5 68.5
## noc 64.4 1.73 41.1 60.9 67.9
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95## contrast estimate SE df t.ratio p.value
## bas - con -1.075 0.287 376 -3.743 0.0006
## bas - noc -0.529 0.287 376 -1.841 0.1159
## con - noc 0.546 0.287 376 1.902 0.1159
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: holm method for 3 tests| Fixed Effects - Heart Rate | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 64.44 | 61.17 – 67.71 | <0.001 |
| Condition-CON | -0.53 | -0.86 – -0.21 | 0.001 |
| Condition-UNCON | 0.54 | 0.22 – 0.87 | 0.001 |
| Random Effects | |||
| σ2 | 6.35 | ||
| τ00 id | 105.85 | ||
| τ00 id.1 | 8.19 | ||
| τ00 id.2 | 13.72 | ||
| ICC | 0.94 | ||
| N id | 42 | ||
| Marginal R2 / Conditional R2 | 0.002 / 0.943 | ||
Heart rates were higher under controllable stress compared to baseline. No other contrasts were significant.
8 MR Parameter Estimates from vmPFC
8.1 Does vmPFC activation modulate ratings?
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: stress ~ condition * beta_weight.z + (1 + condition + run.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 4028.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6061 -0.4029 -0.0261 0.3556 4.1280
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 263.82 16.243
## condition1 180.09 13.420 -0.18
## condition2 69.25 8.322 0.16 -0.78
## run.z 21.82 4.671 0.32 -0.01 0.11
## Residual 86.37 9.293
## Number of obs: 504, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 39.3511 2.4500 41.3034 16.061 < 2e-16 ***
## condition1 -18.6571 2.1586 41.3842 -8.643 8.17e-11 ***
## condition2 7.9990 1.4110 41.4656 5.669 1.23e-06 ***
## beta_weight.z -0.1869 0.5870 402.5588 -0.319 0.7503
## condition1:beta_weight.z 1.4957 0.7777 395.2965 1.923 0.0552 .
## condition2:beta_weight.z -0.4374 0.7754 395.7584 -0.564 0.5730
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 cndtn2 bt_wg. cn1:_.
## condition1 -0.174
## condition2 0.117 -0.732
## beta_wght.z 0.020 -0.057 -0.032
## cndtn1:bt_. -0.066 -0.033 0.077 -0.141
## cndtn2:bt_. 0.005 0.047 -0.017 0.100 -0.516## $emtrends
## condition beta_weight.z.trend SE df lower.CL upper.CL
## bas 1.309 0.915 383 -0.49 3.108
## con -0.624 1.035 403 -2.66 1.410
## noc -1.245 1.001 403 -3.21 0.722
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## bas - con 1.933 1.37 401 1.411 0.3361
## bas - noc 2.554 1.35 406 1.890 0.1429
## con - noc 0.621 1.36 380 0.458 0.8910
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 3 estimates
## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + condition * run.z +
## stress_dur_diff.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2913.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.92054 -0.42509 -0.04567 0.39713 2.86551
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 270.736 16.454
## condition1 135.044 11.621 -0.02
## run.z 32.911 5.737 0.10 -0.28
## stress_dur_diff.z 39.069 6.250 0.08 0.97 -0.43
## condition1:run.z 7.487 2.736 -0.11 0.37 0.15 0.19
## Residual 174.622 13.214
## Number of obs: 336, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.05277 2.65442 40.92761 17.349 < 2e-16 ***
## condition1 -11.29240 1.80418 39.70543 -6.259 2.1e-07 ***
## beta_weight.z -0.06404 1.05586 272.15763 -0.061 0.9517
## condition1:beta_weight.z 2.01487 0.98620 241.14929 2.043 0.0421 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 bt_wg.
## condition1 -0.029
## beta_wght.z 0.009 -0.138
## cndtn1:bt_. -0.081 0.026 0.051
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Groups Name Std.Dev. Corr
## id (Intercept) 16.4541
## condition1 11.6208 -0.024
## run.z 5.7368 0.097 -0.283
## stress_dur_diff.z 6.2505 0.078 0.972 -0.434
## condition1:run.z 2.7363 -0.110 0.366 0.149 0.190
## Residual 13.2145## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + condition + run.z +
## stress_dur_diff.z | id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2916.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7040 -0.4376 -0.0566 0.4348 3.2418
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 269.05 16.403
## condition1 135.19 11.627 -0.02
## run.z 32.38 5.690 0.11 -0.32
## stress_dur_diff.z 44.05 6.637 0.08 0.96 -0.53
## Residual 186.07 13.641
## Number of obs: 336, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.3897 2.6558 40.7747 17.467 < 2e-16 ***
## condition1 -11.8987 1.8302 40.1677 -6.501 9.17e-08 ***
## beta_weight.z 0.2606 1.0645 276.8869 0.245 0.8068
## condition1:beta_weight.z 2.0794 0.9721 264.1351 2.139 0.0333 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 bt_wg.
## condition1 -0.036
## beta_wght.z 0.014 -0.139
## cndtn1:bt_. -0.070 -0.004 0.018
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## helplessness ~ condition * beta_weight.z + (1 + condition + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 2932.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8579 -0.5138 -0.0332 0.4808 3.4685
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 263.79 16.241
## condition1 128.66 11.343 -0.03
## stress_dur_diff.z 40.39 6.355 0.05 1.00
## Residual 227.53 15.084
## Number of obs: 336, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 45.363 2.672 41.047 16.975 < 2e-16 ***
## condition1 -10.346 1.854 40.075 -5.580 1.83e-06 ***
## beta_weight.z -1.298 1.059 279.951 -1.226 0.221
## condition1:beta_weight.z 2.346 1.034 290.011 2.270 0.024 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 bt_wg.
## condition1 -0.053
## beta_wght.z -0.005 -0.106
## cndtn1:bt_. -0.070 -0.005 0.014
## convergence code: 0
## boundary (singular) fit: see ?isSingular## Fitting one lmer() model. [DONE]
## Calculating p-values. [DONE]## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: helplessness ~ condition * beta_weight.z + (1 + stress_dur_diff.z |
## id)
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 10000))
##
## REML criterion at convergence: 3007.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.88000 -0.52787 -0.00622 0.61977 2.43798
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 182.3 13.50
## stress_dur_diff.z 103.1 10.15 -0.15
## Residual 370.6 19.25
## Number of obs: 336, groups: id, 42
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.611 2.677 37.022 17.413 < 2e-16 ***
## condition1 -10.004 1.078 293.217 -9.284 < 2e-16 ***
## beta_weight.z -0.453 1.288 322.535 -0.352 0.72535
## condition1:beta_weight.z 3.082 1.097 296.196 2.808 0.00531 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) cndtn1 bt_wg.
## condition1 0.000
## beta_wght.z -0.001 -0.224
## cndtn1:bt_. -0.074 -0.011 0.049## $emtrends
## condition beta_weight.z.trend SE df lower.CL upper.CL
## con 2.63 1.74 314 -0.802 6.060
## noc -3.53 1.66 314 -6.803 -0.266
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## con - noc 6.16 2.2 296 2.805 0.0054
##
## Degrees-of-freedom method: kenward-roger
| Fixed Effects - Helplessness | |||
|---|---|---|---|
| Predictors | Estimates | 95% CI | p |
| Intercept | 46.61 | 41.36 – 51.86 | <0.001 |
| Condition | -10.00 | -12.12 – -7.89 | <0.001 |
| Beta Weight | -0.45 | -2.98 – 2.07 | 0.725 |
| Condition x Beta Weight | 3.08 | 0.93 – 5.23 | 0.005 |
| Random Effects | |||
| σ2 | 370.61 | ||
| τ00 id | 182.35 | ||
| τ11 id.stress_dur_diff.z | 103.09 | ||
| ρ01 id | -0.15 | ||
| ICC | 0.33 | ||
| N id | 42 | ||
| Marginal R2 / Conditional R2 | 0.168 / 0.442 | ||
VmPFC activation modulated helplessness ratings for uncontrollable stress, not for controllable stress. For uncontrollable stress, higher beta weights were linked to lower helplessness ratings.
9 Correction for Multiple Dependent Variables
## DV p.orig Bonferroni
## 2 helplessness 0.0001 0.0005
## 3 RT 0.0001 0.0005
## 4 correct 0.0073 0.0365
## 1 stress 0.0845 0.4225
## 5 hr 0.1159 0.579510 Figures for Paper
